A torus worm high-efficiency turning process and method

Abstract

The application discloses a high-efficiency turning process and method for a torus worm, and the machining process route and method are as follows: a diamond turning tool is selected to perform rough machining under the precondition that the main shaft is positively rotated; a parting turning tool is selected to perform semi-finishing and finishing of a working tooth surface under the condition that the main shaft is positively rotated; and the parting turning tool is selected to perform semi-finishing and finishing of a non-working tooth surface under the condition that the main shaft is reversely rotated. Since the diamond turning tool has an axial bearing capacity far greater than that of the parting tool, a larger cutting area and a smaller number of tool paths can be selected than the parting tool, so that the low-efficiency problem of the traditional parting tool in machining the torus worm is broken through; meanwhile, the larger nominal clearance angle of the diamond turning tool can make the working clearance angle far away from 0 degree in the turning process, so that the cutting edge can smoothly participate in cutting; in the semi-finishing and finishing process, the main shaft is reversely rotated to cut the non-working tooth surface, so that the working clearance angle of the parting turning tool is greater than the nominal clearance angle, and thus the working clearance angle is far away from 0 degree, so that the machining surface quality of the worm is improved.

Description

Technical Field

[0001] This invention belongs to the field of CNC machining and relates to a high-efficiency turning process and method for toroidal worm gears. Background Technology

[0002] Toroidal worm gear pairs belong to the category of worm gear drives. Compared with ordinary worm gear drives, toroidal worm gear drives have advantages such as instantaneous double-line contact, wide working tooth surface, large contact point normal velocity and comprehensive radius of curvature, good lubrication conditions, strong load-bearing capacity, low contact stress, and long service life. Based on these advantages, toroidal worm gear drives are widely used in metallurgy, shipbuilding, aerospace, and other fields. Currently, besides processing using special-purpose machines, general-purpose machine tools are also the main method for forming this type of worm. The patent (A High-Efficiency Precision CNC Turning Method for an Involute Enveloping Toroidal Worm, CN110421217B) uses a parting tool to turn this type of worm, and uses the same type of parting tool for roughing, semi-finishing, and finishing. All turning processes are performed using forward spindle rotation. However, this method also has its shortcomings: since the cutting tool cannot withstand too much axial force, the cutting allowance of each cut during roughing cannot be too large, which will inevitably lead to an increase in the number of toolpaths and reduce machining efficiency; secondly, during the turning of the toroidal worm, the working clearance angle of the cutting edge cutting the non-working tooth surface is much lower than the nominal clearance angle, and there are even cases where the working clearance angle is negative, which causes the cutting edge to be unable to participate in the work, turning from cutting to extrusion, and even causing the cutting tool to deform, affecting the machining quality; To overcome the aforementioned difficulties, this patent addresses the issue from the following aspects: First, a rhomboid turning tool is used for roughing the worm gear. Second, a parting-off tool is used for semi-finishing and finishing. The difference from traditional processes is that a spindle reversal strategy is employed when cutting non-working tooth surfaces. This process and method offer the following advantages: Because the rhomboid turning tool has a much greater axial load-bearing capacity than a parting-off tool, a larger cutting area can be selected to improve machining efficiency; using a rhomboid tool for roughing effectively reduces the number of toolpaths; the nominal clearance angle of the rhomboid turning tool can be much larger than that of the parting-off tool, and even if the working clearance angle is much smaller than the nominal clearance angle during cutting, it will not approach 0 degrees, which helps protect the tool; during semi-finishing and finishing, although a parting-off tool is used for cutting, the spindle can be reversed to cut non-working tooth surfaces, making the working clearance angle of the parting-off tool larger than the nominal clearance angle, avoiding large axial deformation of the parting-off tool, and thus improving the surface finish of the worm gear. Summary of the Invention

[0003] The main purpose of this invention is to solve the problems of machining defects and hidden dangers that may occur during the turning of toroidal worm gears using a parting tool, so as to improve the surface quality and efficiency of machining.

[0004] The technical solution of this invention is to use a rhomboid turning tool for roughing, and a parting-off turning tool for semi-finishing and finishing. First, based on the specific parameters of the worm, the mathematical expression of the tooth surface of the toroidal worm is solved; then, the worm is rotated around the z-axis, and the value at any moment of rotation is obtained. t The intersection of the worm tooth surface and the coordinate plane (XOZ) is taken as the worm's cross-section; then, with the z-axis as the center of symmetry, the cross-section data is... x The negative part is symmetrical to x Positive semi-axis region; extract the tangent direction at any point of the cross section and calculate the cutting direction and its relationship with the cross section. x The included angle of the axis. Determine the relationship between this included angle and the half angle of the rhombus cutter tip. If the included angle is smaller than the half angle of the rhombus cutter tip, the tool position point is distributed along the extension direction of the rhombus cutter edge line. If the included angle is larger than the half angle of the rhombus cutter tip, the tool position point is located on the offset curve of the cross section. During semi-finishing and finishing processes, the working tooth surface is machined by rotating the spindle forward, and the non-working tooth surface is machined by rotating the spindle in reverse. The specific steps are as follows: A high-efficiency turning process and method for toroidal worm gears includes the following steps: S1. Establish the moving and fixed coordinate systems of the worm gear and the worm respectively, derive the coordinate transformation matrix between each coordinate system, and derive the mathematical model of the working tooth surface and non-working tooth surface of the worm based on this. Worm gear fixed coordinate system: represented as {O0| X 0 Y 0 Z 0 The origin is located at the center of the worm gear base circle. Y 0 The shaft is parallel to the worm axis. Z 0 The shaft passes through the center of the worm gear's base circle and points vertically upwards. X 0 The direction of the axis is determined by the right-hand rule; Worm gear moving coordinate system: represented as {O 0d | X 0d Y 0d Z 0d}, origin and Z 0d axis and {O0| X 0 Y 0 Z 0 The origin and Z 0It shares the same axis, is fixedly connected to the worm gear, and rotates synchronously with the worm gear around its axis; initially, it coincides with the fixed coordinate system of the worm gear. Worm gear fixed coordinate system: represented as {O1| X 1 Y 1 Z 1 The origin is located at the center of the cross-sectional circle of the worm's throat. X 1 shaft and X 0 The axes are parallel. Z 1 The shaft is along the worm gear axis. Y 1 The direction of the axis is determined by the right-hand rule; Worm gear moving coordinate system: represented as {O 1d | X 1d Y 1d Z 1d}, origin and Z 1d axis and {O1| X 1 Y 1 Z 1 The origin and Z 1 It shares the same axis, is fixedly connected to the worm, and rotates synchronously with the worm around its axis; initially, it coincides with the worm's fixed coordinate system. Because the worm's parent plane is tangent to the worm wheel's base cylinder and is Z 0 The axis forms an angle Then any point P on the parent plane of the worm 0d In the worm gear moving coordinate system {O 0d | X 0d Y 0d Z 0d The expression in} is: in, The base circle diameter of the worm gear is... and The range is Parameters; Point P 0d In the worm gear fixed coordinate system {O0| X 0 Y 0Z 0} is represented as Its expression is: in, It is {O0| X 0 Y 0 Z 0} and {O 0d | X 0d Y 0d Z 0d The homogeneous transformation matrix between} It is the worm gear mother plane about the worm wheel fixed coordinate system {O0| X 0 Y 0 Z 0}of Z 0 Angular velocity of the axis of rotation, t It is the worm gear mother plane about the worm wheel fixed coordinate system {O0| X 0 Y 0 Z 0}of Z 0 Axis rotation The time taken to adjust the angle; Point P0 in the worm gear's fixed coordinate system {O1| X 1 Y 1 Z 1 In the}, it is represented as P1, and its expression is: in, It is {O0| X 0 Y 0 Z 0} and {O1| X 1 Y 1 Z 1 The homogeneous transformation matrix between} a It is the distance between O1 and O0; Point P1 is in the moving coordinate system {O} of the worm gear1d | X 1d Y 1d Z 1d In}, it is represented as P 1d Its expression is: in, It is {O 1d | X 1d Y 1d Z 1d} and {O1| X 1 Y 1 Z 1 The homogeneous transformation matrix between} It is the angular velocity of the worm gear rotating about its main axis. t The worm rotates around its main axis. The time taken to adjust the angle; The derivation of the equation for the working tooth surface of the worm gear is as follows: In the worm gear moving coordinate system {O 0d | X 0d Y 0d Z 0d}midpoint normal vector The calculation equation is as follows: In the fixed coordinate system {O1| X 1 Y 1 Z 1 In the equation, the relative velocity vector is represented as: The calculation equation is: Will From the worm gear's fixed coordinate system {O1| X 1 Y 1 Z 1 Transform to the worm gear moving coordinate system {O 0d | X 0d Y0d Z 0d In}, it is represented as The calculation equation is as follows: According to the meshing equation Derive parameters μ for: in, The transmission ratio is calculated using the following formula: ; The equation of the working tooth surface of the worm gear in the moving coordinate system {O 0d | X 0d Y 0d Z 0d In}, it is represented as: The equations for the non-working tooth surfaces of the worm gear are derived using the same steps: in, This is the worm gear tooth thickness coefficient; S2. Use a diamond-shaped turning tool to rough machine the toroidal worm gear; To avoid interference, in X 1O1 Z 1 In the plane, half angle of the knife tip It should be in the fixed coordinate system of the worm gear X The angle between axis 1 and the tangent at any point on the worm gear tooth surface The minimum value is close; based on the homogeneous transformation matrix obtained in step S1. , By combining the equation of the worm tooth surface, we obtain the equation of the worm tooth surface with... X 1O1 Z 1 The intersection of the planes is: assumed and For the two points on the intersection line that are sufficiently close, and They are respectively and Given the parameters, the coordinates of the two points are obtained according to the worm gear tooth surface equation: Then angle The following formula is used to calculate: For the non-working tooth surface of the toroidal worm, there exists... Similar angles Choose a smaller angle as ,Right now: The angle between the cutting plane and the side surface of the lathe tool is defined as the working clearance angle, denoted as: The following is the derivation of the working angle. The calculation equation; The equation for calculating the cutting plane is: in, It is a point on the blade. yes The combined velocity vector, The direction vector of the cutting edge; The calculation equation is as follows: in, It's the point on the blade. speed, It is a point The velocity along the worm axis, It is a point Along {O1| X 1 Y 1 Z 1 The velocity along the X1 axis in the equations are as follows: in, d p For point The distance to the worm axis. f 1 is a point Feed per revolution along the worm axis f 2 For point Along {O1| X 1 Y 1 Z 1 The feed per revolution of the X1 axis in}; Side of the lathe tool The equation expressing this is: in, It is the normal vector of the back face; The calculation equation is as follows: S3. Design the roughing tool path; In {O1| X 1 Y 1 Z 1 The intersection profile of the toroidal worm tooth surface and the plane X1O1Z1 at any given time is determined in the formula}. In {O1| X 1 Y 1 Z 1 In}, time t Below, the toroidal worm gear tooth surface The expression is: When the plane containing the axis of the planar toroidal worm intersects the worm, the resulting cross-section has a series of tooth profiles. This cross-section is divided into several sections, and the intersection points are obtained on these sections. The expression is: Among them, in {O1| X 1 Y 1 Z 1}middle, It is the first Normal vector of each cross section It is the first The vector containing the points on each cross section yes The angle between the x and x vectors; The mathematical model of the tooth profile where the toroidal worm tooth surface intersects the plane X1O1Y1 is as follows: in, For the toroidal worm gear in {O1| X 1 Y 1 Z 1 The tooth surface in} is expressed as: For each tooth profile of the toroidal worm gear, the corresponding positions are connected by G32 CNC code instructions to form the tool path; S4. Use a parting tool to perform semi-finishing and finishing on the toroidal worm; during the semi-finishing and finishing processes, the spindle rotates forward when turning the working tooth surface of the toroidal worm and rotates backward when turning the non-working tooth surface of the toroidal worm. The position of the cutting tool for each tooth profile of the toroidal worm is determined using the following method: Discrete time slots based on the rotation angle of the worm. t span Divided into a series of time periods, the equation is as follows: in, N It refers to the number of time periods; A mathematical model of the tooth profile where the toroidal worm tooth surface intersects the plane X1O1Y1 is used to obtain any time... t The tooth profile of the lower toroidal worm, time t and included angle The expression is: in, j yes j th Each time point; M It is the maximum number of tooth profiles in the cross-section at any given time; For the working tooth surface, The tooth profile is divided into the tooth tip circle and the point. Between, points The two parts between the tooth root circle; exist At that point, the cutting direction of the tooth profile and x The included angle of the shaft is equal to the half angle of the rhomboid turning tool; at the tooth tip circle and point The portion between these points represents the first part of the cutting tool position. The tangent vector at any point on the tooth profile is obtained from the section, and the expression is assumed to be: in, Vx ( r )and Vz ( r ) are respectively V ( r The x-coordinate components and z-coordinate components of ( ); The expression for the normal vector at this point is: knife point Determined as: in, , r a The radius of the worm gear tooth tip circle is... r1 The radius of the arc of the current roughing trajectory. It is the allowance during the rough turning process; The curve formed by connecting these tool points is the first part, with a tooth profile offset distance of [missing information]. The offset curve, R The radius of the tip of the rhomboid turning tool; At point The portion between the tooth root circle and the tooth root circle is the second part of the tool position point, and the curve formed by these tool position points is... The offset line of the tangent Its expression is: in, yes i The position of the th cutting tool along the right cutting edge vector The distance to the center of the blade tip, the vector of the right blade. The expression is: In order to determine We need to discuss two cases regarding turning: Category 1: A diamond-shaped turning tool cannot move to the root circle without removing material that should belong to the worm gear. Described as: in, yes Bias point, Let be a point on a non-working tooth surface, satisfying the sum of the tangent vectors at that point. x The included angle of the shaft is equal to half the angle of the rhomboid turning tool. These are points on the tooth tip circle and on the working tooth profile; The expression is: The expression is: The second type: A rhomboid turning tool can move to the root circle without removing material that should belong to the worm gear. The determining equation is: The third part defines the tool position when the cutting tool moves along the root circle. The expression is: in, It is the first iThe distance from the position of each cutting tool along the right cutting edge vector to the center of its tool tip circle. It is a parameter The maximum value, r f The radius of the worm gear root circle is... w These are the roughing trajectory parameters; S5. Design the tool path for semi-finishing; Based on the finishing allowance, the tooth surface profile is offset to form a profile offset curve; then, based on the tool position point of roughing, a roughing residual curve is formed; the two are calculated in the worm gear fixed coordinate system. z The deviation in direction is finally divided by the axial cutting depth per cut in semi-finishing. This forms the semi-finishing toolpath; the specific steps are as follows: First, calculate the distance from a point on the tooth surface offset curve to the origin, specifically the radius d. r It can be expressed by the following formula: Let be a point on the cross-sectional offset curve. Let be the origin of the moving coordinate system of the worm gear; therefore, the radius d r The number of tool positions is: in, This is a rounding function. The axial cutting depth of the cutting tool, point Containing point The intersection point of the straight line parallel to the z-axis and the roughing residual curve; S6. Design the finishing tool path; During the finishing process, the tool positions corresponding to each cross-section are connected to form the finishing tool path; Finishing tool positions The expression is: in, It is the radius of the cutting blade tip. Let be a point on the cross section of the tooth surface.

[0005] The beneficial effects of the present invention are as follows: The method of the present invention can effectively reduce the number of tool positions and machining time, and the planning method proposed in the present invention can effectively avoid the situation where the working back angle of the tool is negative during the machining process. Attached Figure Description

[0006] Figure 1 This is the coordinate system definition for solving the worm gear surface, where O0 and O 0d Overlap, is {O0| X0 Y 0 Z 0} and {O 0d | X 0d Y 0d Z 0d The origin of} X 0 , Y 0 , Z 0 and X 0d , Y 0d , Z 0d These correspond to the three components of the coordinate system; similarly, O1 and O 1d Overlap, is {O1| X 1 Y 1 Z 1} and {O 1d | X 1d Y 1d Z 1d The origin of} X 1 , Y 1 , Z 1 and X 1d , Y 1d , Z 1d These correspond to the three components of the coordinate system; 0 The rotation angle of the turbine moving coordinate system relative to the turbine stationary coordinate system; 1 The rotation angle of the worm's moving coordinate system relative to the worm's stationary coordinate system; 0d The angular velocity of the turbine rotation. 1d The angular velocity of the worm gear is... To generate the angle between the surface and the turbine axis; Figure 2 It involves the extraction and display of data from the worm gear tooth surface; Figure 3 It is the worm gear and at any time X0 O0 Z 0 The line of intersection of planes is called a cross section. In a cross section... The meaning is, The cross section is the current rotation angle. Increase the current rotation angle by 180 degrees. X 0 O0 Z 0 The intersection of the planes; therefore, the tooth surface and X 0 O0 Z 0 The intersection of planes can be understood as the phase difference between the latter and former sections being 180 degrees; Figure 4 These are situations that may occur during the roughing process of a rhombus-shaped cutting tool. 1st This indicates the first cutter point within the cut. i th represents the first th element within the truncated section. i There are a total of [number] knife points, with a total of [number] knife points. NUM There are several tool positions. The first case is (a), where the rhomboid tool cannot completely cut the working tooth surface, but can completely cut the non-working tooth surface; the second case is (b), where the rhomboid tool can completely cut both the working and non-working tooth surfaces; and the last case is (c), where the rhomboid tool cannot completely cut the non-working tooth surface, but can completely cut the working tooth surface. Figure 5 This refers to tool positioning planning during rough machining with a rhombus-shaped turning tool when incomplete removal is required. For the tooth surface offset curve (offset distance is the allowance), the tangent direction at that point is... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; 1st This indicates the first cutter point within the cut. i th represents the first th element within the truncated section. i Each knife point, This is a point on the tooth surface offset curve whose distance from the center is equal to the radius of the tooth tip circle. This is a point on the tooth surface offset curve whose distance from the center of the circle is the radius of the root circle. l This represents the distance the rhombus-shaped cutting tool moves along the edge of the rhombus. Figure 6 The possible situations when a diamond-shaped cutting tool is cutting the tooth root are: (a) it cannot cut the tooth root, and (b) it can cut the tooth root. For the working tooth surface offset curve (offset distance is the allowance), the tangent direction at this point is satisfied with the... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; For the non-working tooth surface offset curve (offset distance is the allowance), the tangent direction at this point is satisfied with... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; for The point after biasing; Figure 7 It is a semi-finishing tooling position customization strategy. For the tooth surface offset curve (offset distance is the allowance), the tangent direction at that point is... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; This is a point on the tooth surface offset curve whose distance from the center is equal to the radius of the tooth tip circle. This is a point on the tooth surface offset curve whose distance from the center of the circle is the radius of the root circle. Let be the direction vector of the rhomboid cutting tool edge. From The intersection point between the straight line along the z-axis and the working tooth surface offset curve. for or The point after bias, r For radius, For radius increment; Figure 8 It is a combination display of cutoffs obtained at different times; Figure 9 It is to solve for the initial machining tool position; Figure 10 This is the roughing toolpath; Figure 11 It is a semi-finishing toolpath, where (a) is the working tooth surface and (b) is the non-working tooth surface; Figure 12 This is the final, completed worm gear. Figure 13 It is the working clearance angle (nominal working clearance angle 15 degrees) of the non-working tooth surface side of the turning tool when the rhomboid turning tool is cutting the non-working tooth surface. α For the working rear angle; Figure 14 It is the working clearance angle (nominal clearance angle is 5 degrees) when machining non-working tooth surfaces using traditional methods. α For the working rear angle; Figure 15 The working clearance angle (nominal clearance angle is 5 degrees) is formed by cutting the non-working tooth surface with a cutter while the spindle is in reverse. α The working angle. Detailed Implementation

[0007] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0008] Turning on a general-purpose CNC lathe is one of the common methods for machining toroidal worm gears. The first step is to solve for the mathematical expression of the toroidal worm gear tooth surface based on the specific parameters of the worm gear. Then, the worm gear is rotated around the z-axis, and the rotation time at any moment is calculated.t The intersection of the worm tooth surface and the coordinate plane (XOZ) is taken as the worm's cross-section; then, with the z-axis as the center of symmetry, the cross-section data is... x The negative part is symmetrical to x Positive semi-axis region; extract the tangent direction at any point of the cross section and calculate the cutting direction and its relationship with the cross section. x The included angle of the axis. Determine the relationship between this included angle and the half angle of the rhombus cutter tip. If the included angle is smaller than the half angle of the rhombus cutter tip, the tool position point is distributed along the extension direction of the rhombus cutter edge line. If the included angle is larger than the half angle of the rhombus cutter tip, the tool position point is located on the offset curve of the cross section. During semi-finishing and finishing processes, the working tooth surface is machined by rotating the spindle forward, and the non-working tooth surface is machined by rotating the spindle in reverse. The specific steps are as follows: 1. A high-efficiency turning process and method for toroidal worm gears, characterized by comprising the following steps: S1. Establish the moving and fixed coordinate systems of the worm gear and the worm respectively, derive the coordinate transformation matrix between each coordinate system, and derive the mathematical model of the working tooth surface and non-working tooth surface of the worm based on this. S2. Use a diamond-shaped turning tool to rough machine the toroidal worm gear; S3. Design the roughing tool path; S4. Use a parting tool to perform semi-finishing and finishing on the toroidal worm. During the semi-finishing and finishing processes, the spindle rotates forward when turning the working tooth surface of the toroidal worm and reverses when turning the non-working tooth surface of the toroidal worm. S5. Design the tool path for semi-finishing; S6. Design the finishing tool path.

[0009] 2. For example Figure 1 As shown, the moving and fixed coordinate systems of the worm gear and the worm are established respectively, the coordinate transformation matrix between each coordinate system is derived, and the mathematical models of the working tooth surface and non-working tooth surface of the worm are derived accordingly. 3. By deriving the tooth surface equation and solving for the points on the tooth surface, we can obtain... Figure 2 The data for the points on the tooth surface shown are as follows: the left side is the working tooth surface, and the right side is the non-working tooth surface.

[0010] 4. Main parameters of rhomboid turning tools and The method for determining it is as follows: To avoid interference, in X 1O1 Z 1 In the plane, half angle of the knife tip It should be in the fixed coordinate system of the worm gear X The angle between axis 1 and the tangent at any point on the worm gear tooth surface The minimum value is close. According to the homogeneous transformation matrix... and By combining the equation of the worm tooth surface, we can obtain the equation of the worm tooth surface with... X 1O1 Z 1 The intersection of planes, such as Figure 3 As shown, in the cross section The meaning is, The cross section is the current rotation angle. Increase the current rotation angle by 180 degrees. X 0 O0 Z 0 The line of intersection of the planes. Therefore, the tooth surface and... X 0 O0 Z 0 The intersection of planes can be understood as a cross-section where the phase difference between the two cross-sections is 180 degrees. This cross-section can be expressed by the following formula: 5. During the roughing process, the tool path is determined according to the following method: In {O1| X 1 Y 1 Z 1 The intersection profile of the toroidal worm tooth surface and the plane X1O1Z1 at any given time is determined in the formula.

[0011] In {O1| X 1 Y 1 Z 1 In}, time t Below, the toroidal worm gear tooth surface The expression is: When the plane containing the axis of the toroidal worm intersects the worm, the resulting cross-section has a series of tooth profiles. This cross-section can be divided into several sections, such as... Figure 3 As shown, in the cross section The meaning is, The cross section is the current rotation angle. Increase the current rotation angle by 180 degrees. X 0 O0 Z 0 The line of intersection of the planes. Therefore, the tooth surface and... X 0 O0 Z 0The intersection of planes can be understood as a 180-degree phase difference between the subsequent section and the preceding section. Based on this, the roughing tool path can be solved.

[0012] 6. Determine the position of the cutting tool for each tooth profile of the toroidal worm gear using the following method: like Figure 5 As shown, where, For the tooth surface offset curve (offset distance is the allowance), the tangent direction at that point is... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; 1st This indicates the first cutter point within the cut. i th represents the first th element within the truncated section. i Each knife point, This is a point on the tooth surface offset curve whose distance from the center is equal to the radius of the tooth tip circle. This is a point on the tooth surface offset curve whose distance from the center of the circle is the radius of the root circle. l This represents the distance the rhombus-shaped cutting tool moves along the edge of the rhombus. In order to determine Turning needs to be discussed in two categories, such as Figure 6 As shown, (a) cannot cut the tooth root, and (b) can cut the tooth root. For the working tooth surface offset curve (offset distance is the allowance), the tangent direction at this point is satisfied with the... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; For the non-working tooth surface offset curve (offset distance is the allowance), the tangent direction at this point is satisfied with... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; for The point after bias, w It is the arc length between the two cutter points at the tooth root offset curve.

[0013] Category 1: A diamond-shaped cutting tool cannot move to the root circle without removing material that should belong to the worm gear. It can be described as: in: yes Bias point, Let be a point on a non-working tooth surface, satisfying the sum of the tangent vectors at that point. x The included angle of the shaft is equal to half the angle of the rhomboid turning tool. These are points on the tooth tip circle and on the working tooth profile; The expression is: The expression is: The second type: A rhomboid turning tool can move to the root circle without removing material that should belong to the worm gear. The determining equation is: The third part defines the tool position when the cutting tool moves along the root circle. The expression is: in, It is the first i The distance from the position of each cutting tool along the right cutting edge vector to the center of its tool tip circle. It is a parameter The maximum value, r f The radius of the worm gear root circle is... w These are the roughing trajectory parameters; 7. During the semi-finishing process, determine the tool path as follows: Based on the finishing allowance, the tooth surface profile is offset to form a profile offset curve; then, based on the tool position point of roughing, a roughing residual curve is formed; the two are calculated in terms of... z The deviation in direction is finally divided by the axial cutting depth per cut in semi-finishing. This will generate a semi-finishing toolpath.

[0014] like Figure 7 As shown, where, For the tooth surface offset curve (offset distance is the allowance), the tangent direction at that point is... x The included angle of the axis is the point where the tip of the rhomboid turning tool is half an angle; This is a point on the tooth surface offset curve whose distance from the center is equal to the radius of the tooth tip circle. This is a point on the tooth surface offset curve whose distance from the center of the circle is the radius of the root circle. Let be the direction vector of the rhomboid cutting tool edge. From The intersection point of the straight line extending along the z-axis and the working tooth surface offset curve. for or The point after bias, r For radius, This is the radius increment; after calculating the radius... r After determining the number of tool positions at the tool location point, for The radius machining toolpath can be calculated by applying an offset; then, the next radius can be calculated. The semi-finishing tool position is obtained by sequentially cycling through the position points.

[0015] 8. During the finishing process, connect the tool points corresponding to each cross-section to form the finishing tool path; The present invention has the following significant effects: it can effectively reduce the number of tool positions, reduce machining time, and improve machining efficiency; at the same time, the planning method proposed in this method can effectively avoid the working back angle of the tool becoming negative during the machining process.

[0016] Example: The following parameters are selected as the parameters for the toroidal worm gear: 4 degrees The base circle radius is 70 mm. The root radius is 104 mm. The tooth tip circle radius is 99 mm. The center distance is 127 mm. Based on the known information and the calculation in step 3, the tooth surface data of the worm is obtained, such as... Figure 2 As shown; further, solve for the intercept shape, as follows: Figure 8 The diagram shows the combination of cross-sections of the tooth surface at different times; then, with the z-axis as the axis of symmetry, [the following is a partial translation of the original text]. x The negative half-axis section is symmetrically shaped to the positive half-axis region; then, the roughing tool position point is calculated according to step 6, and the result is as follows. Figure 9 As shown, during the initial machining process, the tool position on the right side of the worm cannot completely contact the working tooth surface, but it can completely contact the non-working tooth surface. For the left side of the worm, the diamond-shaped cutting tool can completely contact the working tooth surface but cannot contact the non-working tooth surface. However, for the middle section, the diamond-shaped cutting tool can contact both the working and non-working tooth surfaces. This phenomenon is observed in… Figure 4 This is also reflected in the process; finally, the roughing toolpath is generated, such as... Figure 10 As shown. Next, calculate the semi-finishing trajectory according to step 7, as follows... Figure 11 As shown; finally, according to step 8, fine processing is performed, and the processing result is shown. Figure 13 It was displayed in the middle.

[0017] In this example, there are a total of 45 roughing toolpaths (20 radial layers and 5 toolpaths for the tooth root circle); in this example, there are a total of 60 toolpaths for semi-finishing, which reduces the cutting distance by about half compared to traditional semi-finishing; the number of toolpaths required for roughing and semi-finishing using traditional cutting (20 radial layers for each cross section, 20 axial layers at the tooth tip circle, and 2 at the tooth root circle) is approximately 180. Assuming that the running time of each trajectory is the same (in fact, the radius machining trajectory of this invention only travels about half the length of the traditional machining trajectory, as shown in 11), the number of toolpaths in this invention is reduced by 180-105 = 75, and the efficiency is improved by 75 / 180 = 41.67%.

[0018] Additionally, when using a rhomboid cutting tool with a nominal clearance angle of 15 degrees to cut material on the non-working tooth surface (at a speed of 800 rpm), the working clearance angle decreases, but only to a minimum of about 11.7 degrees, a reduction of 3.3 degrees, far from 0 degrees; when using a parting tool with a nominal clearance angle of 5 degrees to cut the non-working tooth surface while the spindle is rotating clockwise, the resulting working clearance angle is as follows... Figure 13 As shown, the working clearance angle is much smaller than the nominal clearance angle (5 degrees), decreasing by 3.5 degrees, and the working clearance angle is close to 0 degrees. If the nominal clearance angle of the cut-off tool is less than 3.5 degrees, then the working clearance angle will definitely be negative. When cutting non-working tooth surfaces with the cut-off tool while the spindle is in reverse, the working clearance angle is greater than the nominal clearance angle, such as... Figure 15 As shown, machining can be performed efficiently when the spindle is far from 0 degrees. Therefore, using spindle reversal for semi-finishing and finishing of non-working tooth surfaces can effectively prevent the working clearance angle from decreasing.

Claims

1. A high-efficiency turning process for toroidal worm gears, characterized in that, Includes the following steps: S1. Establish the moving and fixed coordinate systems of the worm gear and the worm respectively, derive the coordinate transformation matrix between each coordinate system, and derive the mathematical model of the working tooth surface and non-working tooth surface of the worm based on this. Worm gear fixed coordinate system: represented as {O0| X 0 Y 0 Z 0 The origin is located at the center of the worm gear base circle. Y 0 The shaft is parallel to the worm axis. Z 0 The shaft passes through the center of the worm gear's base circle and points vertically upwards. X 0 The direction of the axis is determined by the right-hand rule; Worm gear moving coordinate system: represented as {O 0d | X 0d Y 0d Z 0d }, the origin and Z 0d axis and {O0| X 0 Y 0 Z 0 The origin and Z 0 It shares the same axis, is fixedly connected to the worm gear, and rotates synchronously with the worm gear around its axis; initially, it coincides with the fixed coordinate system of the worm gear. Worm gear fixed coordinate system: represented as {O1| X 1 Y 1 Z 1 The origin is located at the center of the cross-sectional circle of the worm's throat. X 1 shaft and X 0 The axes are parallel. Z 1 The shaft is along the worm axis. Y 1 The direction of the axis is determined by the right-hand rule; Worm gear moving coordinate system: represented as {O 1d | X 1d Y 1d Z 1d }, the origin and Z 1d axis and {O1| X 1 Y 1 Z 1 The origin and Z 1 It shares the same axis, is fixedly connected to the worm, and rotates synchronously with the worm around its axis; initially, it coincides with the worm's fixed coordinate system. Because the worm's parent plane is tangent to the worm wheel's base cylinder and is Z 0 The axis forms an angle Then any point P on the parent plane of the worm 0d In the worm gear moving coordinate system {O 0d | X 0d Y 0d Z 0d The expression in} is: in, The base circle diameter of the worm gear is... and The range is Parameters; Point P 0d In the worm gear fixed coordinate system {O0| X 0 Y 0 Z 0 } is represented as Its expression is: in, It is {O0| X 0 Y 0 Z 0 } and {O 0d | X 0d Y 0d Z 0d The homogeneous transformation matrix between} It is the worm gear mother plane about the worm wheel fixed coordinate system {O0| X 0 Y 0 Z 0 }of Z 0 Angular velocity of the axis of rotation, t It is the worm gear mother plane about the worm wheel fixed coordinate system {O0| X 0 Y 0 Z 0 }of Z 0 Axis rotation The time taken to adjust the angle; Point P0 in the worm gear's fixed coordinate system {O1| X 1 Y 1 Z 1 In the}, it is represented as P1, and its expression is: in, It is {O0| X 0 Y 0 Z 0 } and {O1| X 1 Y 1 Z 1 The homogeneous transformation matrix between} a It is the distance between O1 and O0; Point P1 is in the moving coordinate system {O} of the worm gear 1d | X 1d Y 1d Z 1d In}, it is represented as P 1d Its expression is: in, It is {O 1d | X 1d Y 1d Z 1d } and {O1| X 1 Y 1 Z 1 The homogeneous transformation matrix between} It is the angular velocity of the worm gear rotating about its main axis. t The worm rotates around its main axis. The time taken to adjust the angle; The derivation of the equation for the working tooth surface of the worm gear is as follows: In the worm gear moving coordinate system {O 0d | X 0d Y 0d Z 0d }midpoint normal vector The calculation equation is as follows: In the worm gear fixed coordinate system {O1| X 1 Y 1 Z 1 In the equation, the relative velocity vector is represented as: The calculation equation is: Will From the worm gear's fixed coordinate system {O1| X 1 Y 1 Z 1 Transform to the worm gear moving coordinate system {O 0d | X 0d Y 0d Z 0d In}, it is represented as The calculation equation is as follows: According to the meshing equation Derive parameters μ for: in, The transmission ratio is calculated using the following formula: ; The equation of the working tooth surface of the worm gear in the moving coordinate system {O 0d | X 0d Y 0d Z 0d In}, it is represented as: The equations for the non-working tooth surfaces of the worm gear are derived using the same steps. in, This is the worm gear tooth thickness coefficient; S2. Use a diamond-shaped turning tool to rough machine the toroidal worm gear; To avoid interference, in X 1O1 Z 1 In the plane, half angle of the knife tip It should be in the fixed coordinate system of the worm gear X The angle between axis 1 and the tangent at any point on the worm gear tooth surface The minimum value is close; based on the homogeneous transformation matrix obtained in step S1. , By combining the equation of the worm tooth surface, we obtain the equation of the worm tooth surface with... X 1O1 Z 1 The intersection of the planes is: assumed and For the two points on the intersection line that are sufficiently close, and They are respectively and Given the parameters, the coordinates of the two points are obtained according to the worm gear tooth surface equation: Then angle The following formula is used to calculate: For the non-working tooth surface of the toroidal worm, there exists... Similar angles Choose a smaller angle as ,Right now: The angle between the cutting plane and the side surface of the lathe tool is defined as the working clearance angle, denoted as: The following is the derivation of the working angle. The calculation equation; The equation for calculating the cutting plane is: in, It is a point on the blade. yes The combined velocity vector, The direction vector of the cutting edge; The calculation equation is as follows: in, It's the point on the blade. speed, It is a point The velocity along the worm axis, It is a point Along {O1| X 1 Y 1 Z 1 The velocity along the X1 axis in the equations are as follows: in, d p For point Distance to the worm axis f 1 is a point Feed per revolution along the worm axis f 2 For point Along {O1| X 1 Y 1 Z 1 The feed per revolution of the X1 axis in}; Side of the lathe tool The equation expressing this is: in, It is the normal vector of the back face; The calculation equation is as follows: S3. Design the roughing tool path; In {O1| X 1 Y 1 Z 1 The intersection profile of the toroidal worm tooth surface and the plane X1O1Z1 at any given time is determined in the formula}. In {O1| X 1 Y 1 Z 1 In}, time t Below, the toroidal worm gear tooth surface The expression is: When the plane containing the axis of the planar toroidal worm intersects the worm, the resulting cross-section has a series of tooth profiles. This cross-section is divided into several sections, and the intersection points are obtained on these sections. The expression is: Among them, in {O1| X 1 Y 1 Z 1 }middle, It is the first Normal vector of each cross section It is the first The vector containing the points on each cross section yes The angle between the x and x vectors; The mathematical model of the tooth profile where the toroidal worm tooth surface intersects the plane X1O1Y1 is as follows: in, For the toroidal worm gear in {O1| X 1 Y 1 Z 1 The tooth surface in} is expressed as: For each tooth profile of the toroidal worm gear, the corresponding positions are connected by G32 CNC code instructions to form the tool path; S4. Use a parting tool to perform semi-finishing and finishing on the toroidal worm; during the semi-finishing and finishing processes, the spindle rotates forward when turning the working tooth surface of the toroidal worm and rotates backward when turning the non-working tooth surface of the toroidal worm. The position of the cutting tool for each tooth profile of the toroidal worm is determined using the following method: Discrete time slots based on the rotation angle of the worm. t span Divided into a series of time periods, the equation is as follows: in, N It refers to the number of time periods; A mathematical model of the tooth profile where the toroidal worm tooth surface intersects the plane X1O1Y1 is used to obtain any time... t The tooth profile of the lower toroidal worm, time t and included angle The expression is: in, j yes j th Each time point; M It represents the maximum number of tooth profiles in the cross-section at any given time. For the working tooth surface, The tooth profile is divided into the tooth tip circle and the point. Between, points The two parts between the tooth root circle; exist At that point, the cutting direction of the tooth profile and x The included angle of the shaft is equal to the half angle of the rhomboid turning tool; at the tooth tip circle and point The portion between these two points represents the first part of the cutting tool position. The tangent vector at any point on the tooth profile is obtained from the section, and the expression is assumed to be: in, Vx ( r )and Vz ( r ) are respectively V ( r The x-coordinate components and z-coordinate components of ( ); The expression for the normal vector at this point is: knife point Determined as: in, , r a The radius of the worm gear tooth tip circle is... r 1 The radius of the arc of the current roughing trajectory. It is the allowance during the rough turning process; The curve formed by connecting these tool points is the first part of the tooth profile offset distance. The offset curve, R The radius of the tip of the rhomboid turning tool; At point The portion between the tooth root circle and the tooth root circle is the second part of the tool position point, and the curve formed by these tool position points is... The offset line of the tangent Its expression is: in, yes i The position of the th cutting tool along the right cutting edge vector The distance to the center of the blade tip, the vector of the right blade. The expression is: In order to determine We need to discuss two cases regarding turning: Category 1: A diamond-shaped turning tool cannot move to the root circle without removing material that should belong to the worm gear. Described as: in, yes Bias point, Let be a point on a non-working tooth surface, satisfying the sum of the tangent vectors at that point. x The included angle of the shaft is equal to half the angle of the rhomboid turning tool. These are points on the tooth tip circle and on the working tooth profile; The expression is: The expression is: The second type: A rhomboid turning tool can move to the root circle without removing material that should belong to the worm gear. The determining equation is: The third part defines the tool position when the cutting tool moves along the root circle. The expression is: in, It is the first i The distance from the position of each cutting tool along the right cutting edge vector to the center of its tool tip circle. It is a parameter The maximum value, r f The radius of the worm gear root circle is... w These are the roughing trajectory parameters; S5. Design the tool path for semi-finishing; Based on the finishing allowance, the tooth surface profile is offset to form a profile offset curve; then, based on the tool position point of roughing, a roughing residual curve is formed; the two are calculated in the worm gear fixed coordinate system. z The deviation in direction is finally divided by the axial cutting depth per cut in semi-finishing. This forms the semi-finishing toolpath; the specific steps are as follows: First, calculate the distance from a point on the tooth surface offset curve to the origin, specifically the radius d. r It can be expressed by the following formula: Let be a point on the cross-sectional offset curve. Let be the origin of the moving coordinate system of the worm gear; therefore, the radius d r The number of tool positions is: in, This is a rounding function. The axial cutting depth of the cutting tool, point Containing point The intersection point of the straight line parallel to the z-axis and the roughing residual curve; S6. Design the finishing tool path; During the finishing process, the tool positions corresponding to each cross-section are connected to form the finishing tool path; Finishing tool positions The expression is: in, It is the radius of the cutting blade tip. Let be a point on the cross section of the tooth surface.

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